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Atkins & de Paula:
Atkins Physical Chemistry 9e
Checklist of key ideas
Chapter 7: Quantum Theory:
Introduction and Principles
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Chapter 7: Quantum Theory: Introduction and Principles
classical mechanics, the laws of motion introduced in the
seventeenth century by Isaac Newton.
quantum mechanics, the laws of motion introduced in thetwentieth century by Heisenberg and Schrdinger.
THE ORIGINS OF QUANTUM MECHANICS
electromagnetic field, an oscillating electric and magnetic
disturbance that spreads as a harmonic wave through space.
electric field, a field that acts on charged particles.
magnetic field, a field that acts on moving charged
particles.
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Chapter 7: Quantum Theory: Introduction and Principles
wavelength,, the peak-to-peak distance of a wave.
frequency,v, the number of times per second that a
displacement returns to its initial value.
wavenumber, v , the reciprocal of the wavelength.
electromagnetic spectrum, the range of frequencies
exhibited by the electromagnetic field and its classificationinto regions.
7.1 The failures of classical physics
black body, an object capable of emitting and absorbing al
frequencies of radiation uniformly.
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Chapter 7: Quantum Theory: Introduction and Principles
7.1 The failures of classical physics (cont)
RayleighJeans law, dE= d, = 8kT/4.
density of states,, the proportionality constant between thrange of wavelengths and the energy density in that range: d
= d.
ultraviolet catastrophe, the divergence of the energydensity of black-body radiation at high frequencies.
quantization of energy, the limitation of energies to discret
values.
Plancks constant, h = 6.626 08 1034 J s.
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Chapter 7: Quantum Theory: Introduction and Principles
Planck distribution, dE=d, = (8hc/5)/(ehc/kT 1).
Dulong and Petits law: the molar heat capacities of all
monatomic solids are the same, and close to 25 J K1
mol1
.
Einstein formula, CV,m = 3Rf,f= (E/T)2{e
_E/2T/(e
_E/T 1)}
Einstein temperature, E = hv/k.
Debye formula, CV,m = 3Rf, ( )
D
34
/
20D
e
3 de 1
xT
x
T x
f x
=
.
7.1 The failures of classical physics (cont..)
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Chapter 7: Quantum Theory: Introduction and Principles
Debye temperature,D = hvD/k.
spectrum, the record of intensity of light transmitted,absorbed, or scattered as a function of frequency,
wavelength, or wavenumber.
spectroscopy, the detection and analysis of a spectrum.
spectroscopic transition, a change of state that gives rise
to a feature in spectrum.
Bohr frequency transition, the relation between the
change in energy and the frequency of the radiation
emitted or absorbed: E= hv.
7.1 The failures of classical physics (cont..)
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Chapter 7: Quantum Theory: Introduction and Principles
7.2 Waveparticle duality
photon, a particle of electromagnetic radiation.
photoelectric effect,
the ejection of electrons from metals when they areexposed to ultraviolet radiation: mev2
= hv .
work function,, the energy required to remove an electron from the
metal to infinity .
DavissonGermer experiment, the diffraction of electrons by a crystal.
electron diffraction, the diffraction of electrons by an object in their path.
de Broglie relation, = h/p.
waveparticle duality, the joint particle and wave character of matter
and radiation.
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Chapter 7: Quantum Theory: Introduction and Principles
THE DYNAMICS OF MICROSCOPIC SYSTEMS
wavefunction,, a mathematical function obtained by solving
the Schrdinger equation and which contains all the dynamical
information about a system.
7.3 The Schrdinger equation
time-independent Schrdinger equation,(
2/2m)(d
2/dx
2) + V(x)= E.
7.4 The Born interpretation of the wavefunctionBorn interpretation, the value of ||
2at a point is proportional
to the probability of finding the particle at that point.
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Chapter 7: Quantum Theory: Introduction and Principles
7.4 The Born interpretation of the wavefunction (cont..)
Born interpretation, the value of ||2
at a point is proportional
to the probability of finding the particle at that point.
probability density, the probability of finding a particle in a
region divided by the volume of the region.
probability amplitude, the square-root of the probability
density (the wavefunction itself).
normalization constant, N= 1/{* dx}1/2.
spherical polar coordinates, the radius r, the colatitude , and
the azimuth . The volume element in spherical coordinates isr2sin drdd.
quantization, confinement of a dynamical observable to
discrete values.
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Chapter 7: Quantum Theory: Introduction and Principles
constraints on the wavefunction, the conditions a
wavefunction must obey (be continuous, have a continuous firs
derivative, be single-valued, and be square-integrable).
QUANTUM MECHANICAL PRINCIPLES
7.5 The information in a wavefunctionnode, a point where a wavefunction passes through zero .
operator, something that carries out a mathematical operation
on a function.
hamiltonian operator, the operator for the total energy of a
system, EH = .
7.4 The Born interpretation of the wavefunction (cont..)
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Chapter 7: Quantum Theory: Introduction and Principles
eigenvalue, the constant in the eigenvalue equation = .
eigenfunction, the function in the eigenvalue equation = .
eigenvalue equation, an equation of the form = .
observable, measurable properties of a system.
position operator, x = x.
momentum operator, px = (/i)d/dx.
hermitian operator, an operator for which it is true that
{ }
= dxdx ijji
7.5 The information in a wavefunction (cont..)
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Chapter 7: Quantum Theory: Introduction and Principles
orthogonal functions, i*j d = 0.
linear combination of two functions, c1f+ c2g.
superposition, a linear combination of wavefunctions.
complete set of functions, functions that can be used to
express any arbitrary function as a linear combination.
expectation value, d= .
7.6 The uncertainty principle
Heisenberg uncertainty principle: it is impossible to
specify simultaneously, with arbitrary precision, both the
momentum and the position of a particle; 21 qp .
7.5 The information in a wavefunction (cont..)
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Chapter 7: Quantum Theory: Introduction and Principles
wave packet, a localized wavefunction formed by
superimposing a series of wavefunctions.complementary observables, observables corresponding
to non-commuting operators.
commuting operators, operators for which 0, 21 = .
commutator,122121
, =
general form of the Heisenberg uncertainty principle:
[ ]2121 ,2
1
7.6 The uncertainty principle (cont..)
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Atomic Units
hartree1J/mol10627.50954.184
al/mol627.5095kc27.21eV:energy14:typermittivivacuum
11029177.54
aradiusBohr:length
1)10(1.602176e:charge
11010938.9m:electronanofmass
12
h
unitatomicSI
3
00
11-
2
2
00
19-
31-
e
==
=
==
=
=
mem
C
kg
e
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